Animation Nodes - Have an effector control the rotation of many objects
Your Question

We can compose a transformation matrix out of the locations, then generate the rotation matrix using the Offset Matrices Node and then set the objects transformations to this new matrices.



Warning - Make sure not change the locations of the matrices or set the locations of the object by mistake to any value.

Recommended

If your objects are exactly the same, then you can replicate them using the Object Instancer node and set their locations using thew Distribute matrices node (See my answer here: Answer):



Note - If the object has modifiers and you want to copy them, use Copy Full Object option in the Object Instancer.

If you objects are different, then you can replace the Object Instancer with the Object From Group just as you did.